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The fourth-order equations arising from this action are complicated and it is difficult to extract details about cosmological evolution from them. 8: Constraints on the dark-energy equation-of-state parameter, as a function of ΩM , assuming a flat universe. These limits are derived from studies of supernovae, CMB anisotropies, measurements of the Hubble constant, large-scale structure, and primordial nucleosynthesis. From [104]. 33 the gravitational Lagrangian takes the Einstein-Hilbert form and the additional degrees of ¨ and H) ˙ are represented by a fictitious scalar field φ.

88) In a more complete description, a fluid will be characterized by quantities in addition to the energy density and pressure. Many fluids have a conserved quantity associated with them and so we will also introduce a number flux density N µ , which is also conserved ∇µ N µ = 0 . (89) For non-tachyonic matter N µ is a timelike 4-vector and therefore we may decompose it as N µ = nU µ . (90) We can also introduce an entropy flux density S µ . This quantity is not conserved, but rather obeys a covariant version of the second law of thermodynamics ∇µ S µ ≥ 0 .

We have chosen the coupling constant µ to be very small, but we have also introduced a new light degree of freedom. Chiba [114] has pointed out that the model with n = 1 is equivalent to Brans-Dicke theory with ω = 0 in the approximation where the potential was neglected, and would therefore be inconsistent with experiment. It is not yet clear whether including the potential, or considering extensions of the original model, could alter this conclusion. 4 Early Times in the Standard Cosmology In the first lecture we described the kinematics and dynamics of homogeneous and isotropic cosmologies in general relativity, while in the second we discussed the situation in our current universe.

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A Chessplaying Astronomer by Edward Winter

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